What is the difference between Bayes-adaptive MDP and a Belief-MDP in Reinforcement Learning?
Both Belief-MDPs and Bayes-Adaptive MDPs (BAMDPs) are special cases of POMDPs and their state space is augmented with a belief over their unobserved/hidden variables.
In a belief-MDP, the hidden variables can change over the course of an episode. (Eg. Both the position and the uncertainty in the position of the robot can vary during an episode).
In a  BAMDP, the hidden variables are usually the attributes of the transition/reward function and are held constant during an episode. (Eg. In a robot locomotion task, ground friction or load - dynamics attributes, current goal location - reward function attributes. Though variables defining these attributes are unknown to the agent and the agent has to infer them, the actual variables remain unchanged during an episode)
References:

M Ghavamzadeh, S Mannor, J Pineau, Aviv Tamar - Bayesian reinforcement learning: A survey. Foundations and Trends in Machine Learning, 8(5-6):359-483, 2015.

L Zintgraf, K Shiarlis, M Igl, S Schulze, Y Gal, K Hofmann, and S Whiteson. Varibad: A very good method for bayes-adaptive deep rl via meta-learning. arXiv preprint arXiv:1910.08348, 2019.